Finite Group Databasebeta

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C3×A4×C269 #23753136

order9684
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C269 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×A4×C269
unambiguous semidirect productC22⋊(C32×C269)
unambiguous semidirect product(C22×C3)⋊(C3×C269)
unambiguous semidirect product(C22×C269)⋊C32
unambiguous semidirect product(C22×C3×C269)⋊C3

Splittings

Fitting, socleC22×C3×C269 ⋊ C3
derived, SylowC22 ⋊ C32×C269
HallC22×C269 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C269A4
commutator, cosocle, hypocenterC22C32×C269
FrattiniC1G
Fitting, socleC22×C3×C269C3
LCSG ▷ C22
UCSC1 ◁ C3×C269

28 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9684, 31);